Orthogonal vectors

Let S be the subspace of all vectors in R4 that are orthogonal to each of the vectors
(0, 4, 4, 2), (3, 4, -2, -4)
What is an example of a matrix for which S is the nullspace?

3. The attempt at a solution

I'm not sure how I should be intepreting the question:

[ 0 ,4 ,4 ,2 ;3, 4, -2, -4] = [ x , y ,z , t] = [ 0 , 0 ]

0x + 4y + 4z + 2t = 0

3x + 4y -2 z -4t = 0

from here I set up an augmented matrix and solve for the set of vectors x ,y ,z ,t? By definition if x, y, z, t results in each linear equation = 0, then, x ,y ,z ,t are vectors with properties of orthogonality?